Free Vibration of Damaged Beam Structure with a Notch Defect

2012 ◽  
Vol 226-228 ◽  
pp. 44-47 ◽  
Author(s):  
Jiang Yi Chen ◽  
Li Ge Fan ◽  
Dong Chen Qin
Keyword(s):  
Damage Identification ◽  
Delta Function ◽  
Theoretical Background ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Beam Structure ◽  
Arbitrary Boundary ◽  
Numerical Examples ◽  
Elastically Supported ◽  
Universal Expression

In this paper, we derive the universal expression of the modal parameters for a damaged beam under arbitrary boundary conditions. The delta function is first employed to describe a notch damage in the beam and consequently to derive the governing equation for the damaged beam. Second, by virtue of the perturbation method, the eigenvalues and the corresponding mode shapes are obtained for the damaged beam. Finally, numerical examples are given for an elastically supported beam. It is believed that the proposed approach could provide the necessary theoretical background for damage identification in beam structures.

Curvature Mode Characteristics of the Simple Beam with a Local Damaged Crack

2010 ◽  
Vol 139-141 ◽  
pp. 2574-2577
Author(s):  
Ying Tie ◽  
Ping Xu ◽  
Jiang Yi Chen
Keyword(s):  
Damage Identification ◽  
Unit Length ◽  
Delta Function ◽  
Theoretical Background ◽  
Second Order ◽  
Mode Shapes ◽  
Damage State ◽  
Linear Combinations ◽  
Mode Characteristics ◽  
Crack Position

General expressions of crack perturbations are given with perturbation method. With the delta function to express the crack position at the simple beam, the expressions of cross-section rotary inertia and mass per unit length of the whole beam are founded, and then the transverse free vibration equation of the simple beam with a damaged crack is established. The first and second order perturbations are considered as the linear combinations of corresponding mode shapes of intact state, according to the boundary conditions, and theoretical solutions about eigenvalues and mode shapes of the damage state are finally obtained. One simple beam is taken as a numerical example to calculate the modal parameters; the effects of first and second order perturbations on the results are compared. It is believed that the approach proposed in this paper could provide the necessary theoretical background for damage identification in simple beam.

scholarly journals Operational modal analysis using lifted continuously scanning laser Doppler vibrometer measurements and its application to baseline-free structural damage identification

2019 ◽  
Vol 25 (7) ◽  
pp. 1341-1364 ◽  
Author(s):  
Y.F. Xu ◽  
Da-Ming Chen ◽  
W.D. Zhu
Keyword(s):  
Structural Damage ◽  
Damage Identification ◽  
Laser Doppler Vibrometer ◽  
Laser Doppler ◽  
Scanning Laser ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Experimental Investigations ◽  
Scanning Laser Doppler Vibrometer ◽  
White Noise Excitation

A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of efficient and spatially dense vibration measurements by sweeping its laser spot along a scan path assigned on a structure. This paper proposes a new operational modal analysis (OMA) method based on a data processing method for CSLDV measurements of a structure, called the lifting method, under white-noise excitation and applies a baseline-free method to identify structural damage using estimated mode shapes from the OMA method. The lifting method enables transformation of raw CSLDV measurements into measurements at individual virtual measurement points, as if the latter were made by use of an ordinary scanning laser Doppler vibrometer in a step-wise manner. It is shown that a correlation function with nonnegative time delays between lifted CSLDV measurements at two virtual measurement points on a structure under white-noise excitation and its power spectrum contain modal parameters of the structure, that is, natural frequencies, modal damping ratios, and mode shapes. The modal parameters can be estimated by using a standard OMA algorithm. A major advantage of the proposed OMA method is that curvature mode shapes associated with mode shapes estimated by the method can reflect local anomaly caused by small-sized structural damage, while those estimated by other existing OMA methods that use CSLDV measurements cannot. Numerical and experimental investigations are conducted to study the OMA method and baseline-free structural damage identification method. In the experimental investigation, effects of the scan frequency of a CSLDV system on the two methods were studied. It is shown in both the numerical and experimental investigations that modal parameters can be accurately estimated by the OMA method and structural damage can be successfully identified in neighborhoods with consistently high values of curvature damage indices.

Operational Modal Analysis and Damage Identification of Structures Undergoing Random Vibration Using a Continuously Scanning Laser Doppler Vibrometer System

2018 ◽  
Author(s):  
Da-Ming Chen ◽  
Y. F. Xu ◽  
W. D. Zhu
Keyword(s):  
Structural Damage ◽  
Damage Identification ◽  
Laser Doppler Vibrometer ◽  
Laser Doppler ◽  
Scanning Laser ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Experimental Investigations ◽  
Scanning Laser Doppler Vibrometer ◽  
White Noise Excitation

A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of efficient and spatially dense vibration measurements by sweeping its laser spot along a scan path assigned on a structure. This paper proposes a new operational modal analysis (OMA) method based on a data processing method for CSLDV measurements of a structure, called the lifting method, under white-noise excitation and applies a baseline-free method to identify structural damage using estimated mode shapes from the OMA method. The lifting method enables transformation of raw CSLDV measurements into measurements at individual virtual measurement points, as if the latter were made by use of an ordinary scanning laser Doppler vibrometer in a step-wise manner. It is shown that a correlation function with non-negative time delays between lifted CSLDV measurements of two virtual measurement points on a structure under white-noise excitation and its power spectrum contain modal parameters of the structure, i.e., natural frequencies, modal damping ratios and mode shapes. The modal parameters can be estimated by using a standard OMA algorithm. A major advantage of the proposed OMA method is that curvature mode shapes associated with mode shapes estimated by the method can reflect local anomaly caused by small-sized structural damage, while those estimated by other existing OMA methods that use CSLDV measurements cannot. Numerical and experimental investigations are conducted to study the OMA method and baseline-free structural damage identification method. In the experimental investigation, effects of the scan frequency of a CSLDV system on the two methods were studied. It is shown in both the numerical and experimental investigations that modal parameters can be accurately estimated by the OMA method and structural damage can be successfully identified in neighborhoods with consistently high values of curvature damage indices.

Damage Identification of Beam Structures Based on Genetic Algorithm and Sensitivity Analysis

2012 ◽  
Vol 455-456 ◽  
pp. 1474-1479
Author(s):  
Tian Li Huang ◽  
Wei Xin Ren
Keyword(s):  
Genetic Algorithm ◽  
Sensitivity Analysis ◽  
Damage Identification ◽  
Identification Problem ◽  
Mode Shapes ◽  
Damage Localization ◽  
Scalar Model ◽  
Beam Structure ◽  
Beam Structures ◽  
Damage Location

Based on the damage scalar model and the sensitivity analysis of frequency and mode shape, the Combined Multiple Damage Location Assurance Criterion (CMDLAC) based on the change of frequencies and mode shapes was proposed. Then, the damage identification problem is transformed to the constrained optimum problem and the genetic algorithm (GA) is adopted for the damage localization of beam structures. At last, the numerical simulation results of a 3-span continuum beam structure verified the proposed method.

Effect of Bass Bar Tension on Modal Parameters of a Violin's Top Plate

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa
Keyword(s):  
Modal Analysis ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Normal Value ◽  
Modal Damping

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).

scholarly journals Comparison of Mode Shapes of Carbon-Fiber-Reinforced Plastic Material Considering Carbon Fiber Direction

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 311
Author(s):  
Chan-Jung Kim
Keyword(s):  
Carbon Fiber ◽  
Modal Analysis ◽  
Dynamic Behavior ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Carbon Fiber Reinforced Plastic ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Fiber Reinforced Plastic ◽  
Reinforced Plastic

Previous studies have demonstrated the sensitivity of the dynamic behavior of carbon-fiber-reinforced plastic (CFRP) material over the carbon fiber direction by performing uniaxial excitation tests on a simple specimen. However, the variations in modal parameters (damping coefficient and resonance frequency) over the direction of carbon fiber have been partially explained in previous studies because all modal parameters have only been calculated using the representative summed frequency response function without modal analysis. In this study, the dynamic behavior of CFRP specimens was identified from experimental modal analysis and compared five CFRP specimens (carbon fiber direction: 0°, 30°, 45°, 60°, and 90°) and an isotropic SCS13A specimen using the modal assurance criterion. The first four modes were derived from the SCS13A specimen; they were used as reference modes after verifying with the analysis results from a finite element model. Most of the four mode shapes were found in all CFRP specimens, and the similarity increased when the carbon fiber direction was more than 45°. The anisotropic nature was dominant in three cases of carbon fiber, from 0° to 45°, and the most sensitive case was found in Specimen #3.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

scholarly journals Modelling of the Coupled Beam-Piezoelectric Material With Hysteresis Non-Linerity Effect

2018 ◽  
Vol 217 ◽  
pp. 02001
Author(s):  
Mohd Hafiz Abdul Satar ◽  
Ahmad Zhafran Ahmad Mazlan
Keyword(s):  
Modal Analysis ◽  
Piezoelectric Material ◽  
Piezoelectric Actuator ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Stress And Strain ◽  
Sinusoidal Voltage ◽  
Correction Algorithm ◽  
Beam Structure ◽  
Piezoelectric Patch

Hysteresis is one of the non-linearity characteristics of the piezoelectric material. This characteristic is important to be characterized since it can affect the performance of the piezoelectric material as sensor or actuator in many applications. In this study, the model of the coupled aluminium beam with single piezoelectric patch material is constructed to investigate the hysteresis effect of the piezoelectric material to the whole beam structure. A P-876 DuraActTM type piezoelectric patch material is used in modelling of the piezoelectric actuator. Firstly, the modal analysis of the coupled beam-piezoelectric actuator is determined to get the natural frequencies and mode shapes. Then, the piezoelectric patch material is investigated in terms of actuator by given a sinusoidal voltage excitation and output in terms of deflection, stress and strain of the piezoelectric actuator are investigated. From the results, it is clear that, the coupled beam-piezoelectric material is affected by the hysteresis of the piezoelectric material and the natural frequencies of the beam structure. This characteristic is important for the piezoelectric actuator manufacturer and by providing the correction algorithm, it can improve the performance of the piezoelectric actuator for many applications.

scholarly journals Measuring the modal parameters of a cultural heritage tower by using strong-motion signals

ACTA IMEKO ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 86 ◽  
Author(s):  
Mariella Diaferio ◽  
Dora Foti ◽  
Nicola Ivan Giannoccaro ◽  
Salvador Ivorra Ivorra
Keyword(s):  
Phase Shift ◽  
Environmental Conditions ◽  
Excitation Frequency ◽  
Strong Motion ◽  
Forced Vibrations ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Vibration Modes ◽  
Experimental Campaign ◽  
Different Levels

This paper presents the dynamic experimental campaign carried out on a stocky masonry clock tower situated in the Swabian Castle of Trani (Italy). The main objective of this paper is, after estimating the main frequencies and vibration modes of the considered structure, defining the transmission of vibrations along the height of the tower by varying the forced frequency at the base. At this aim, short acceleration records have been acquired simultaneously in 20 points of the tower at different levels, due to a series of sinusoidal forced vibrations applied at the base by using a pneumatic shaker device specify designed for the tests. The proposed procedure permit to extract for each monitored point the amplitude of the sinusoidal component related to the excitation frequency and the phase shift due to the structure damping. The results of the proposed procedure are compared with the results of a classical operational modal analysis in environmental conditions in order to demonstrate that the short forced tests permit to classify the typology of the structure mode shapes.

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